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 概率多项式
 probability polynomial
 Probability Polynomial and Its Application 概率多项式及其应用 短句来源
 probabilistic polynomial
 Some Results On Probabilistic Polynomial—time Hierarchy 关于概率多项式时间谱系的一些结果 短句来源
 “概率多项式”译为未确定词的双语例句
 In this paper, they study the structure properties of probabilistic polynomial-time hierarchy and prove the following results . (1) If BP∑_(k+1)~pBP∑_k~p, then PH=BP∑_k~P; 研究概率多项式时间谱系的结构性质,证明了:(1)如果BP∑_(k+1)~pBP∑_k~P,则PH=BP∑∏_K~P; 短句来源 (4)For every n, k≥1,BP∑_n~P(BP∑_k~pBP_k~p)=BP∑_(n+k-1)~p·These results show that the probabilistic polynomial-time hierarchy has the same structure properties as the polynomial-time hierarchy, but they also have diffrence. (4)对任意n,k≥1,BP∑_n~P(BP∑_k~p∩BP∏_k~P)=BP∑_(n+k-1)~P这些结果说明概率多项式时间谱系与多项式时间谱系有相同的结构性盾,但也有差别. 短句来源

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 probabilistic polynomial
 A probabilistic polynomial-time prover with the appropriate trapdoor knowledge is sufficient. This treatment is appropriate for cryptographic settings modeled by probabilistic polynomial-time machines. [ACGS] that the following problems are equivalent by probabilistic polynomial time reductions: (1) given EN(x) find x; (2) given EN(x) predict the least-significant bit of x with success probability 1/2 + 1/poly(n) , where N has n bits. The security guarantee holds with respect to probabilistic polynomial-time adversaries that control the communication channel (between the parties), and may omit, insert, and modify messages at their choice. We introduce generalized notions of low and high complexity classes and study their relation to structural questions concerning bounded probabilistic polynomial-time complexity classes. 更多
 In this paper, they study the structure properties of probabilistic polynomial-time hierarchy and prove the following results .(1) If BP∑_(k+1)~pBP∑_k~p, then PH=BP∑_k~P;(2) If BP∑_k~pBP_k~p,then PH=BP∑_k~p=BP_k~p;(3)For every n, k≥0, BP∑_n~p(BP∑_k~p)=BP∑_(n+k)~P,BP∑_n~P,(BP△_(k+1)~p)=BP∑_(n+k)~p;(4)For every n, k≥1,BP∑_n~P(BP∑_k~pBP_k~p)=BP∑_(n+k-1)~p·These results show that the probabilistic polynomial-time hierarchy has the same structure properties as the polynomial-time hierarchy, but they also have diffrence.... In this paper, they study the structure properties of probabilistic polynomial-time hierarchy and prove the following results .(1) If BP∑_(k+1)~pBP∑_k~p, then PH=BP∑_k~P;(2) If BP∑_k~pBP_k~p,then PH=BP∑_k~p=BP_k~p;(3)For every n, k≥0, BP∑_n~p(BP∑_k~p)=BP∑_(n+k)~P,BP∑_n~P,(BP△_(k+1)~p)=BP∑_(n+k)~p;(4)For every n, k≥1,BP∑_n~P(BP∑_k~pBP_k~p)=BP∑_(n+k-1)~p·These results show that the probabilistic polynomial-time hierarchy has the same structure properties as the polynomial-time hierarchy, but they also have diffrence. 研究概率多项式时间谱系的结构性质,证明了:(1)如果BP∑_(k+1)~pBP∑_k~P,则PH=BP∑∏_K~P;(2)如果BP∑_k~PBP∏_k~P,则;PH=BP∑_K~PP;(3)对任意n,k≥0,BP∑_K~P(BP∑_n~P)=BP∑_(n+k)~p,BP∑_n~P(BP△_(k+1)~P)=BP∑_(n+k)~n;(4)对任意n,k≥1,BP∑_n~P(BP∑_k~p∩BP∏_k~P)=BP∑_(n+k-1)~P这些结果说明概率多项式时间谱系与多项式时间谱系有相同的结构性盾,但也有差别. In this paper,we introduce the terminology of Probability Polynomial and give the probability expression formula for an event in terms of the intersection of several other events in probability space by using contribute principle in combinatorics enumeration.\; 本文引入概率多项式的概念 ,利用组合数学计数理论中“贡献法原理”给出概率空间任一事件的概率由若干事件交的概率表达公式。
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